WIAS Preprint No. 1649, (2011)

Mayer and virial series at low temperature


  • Jansen, Sabine

2010 Mathematics Subject Classification

  • 82B05 82B26


  • classical statistical mechanics, Mayer and virial series, phase transitions




We analyze the Mayer pressure-activity and virial pressure-density series for a classical system of particles in continuous configuration space at low temperature. Particles interact via a finite range potential with an attractive tail. We propose physical interpretations of the Mayer and virial series' radius of convergence, valid independently of the question of phase transition: the Mayer radius corresponds to a fast increase from very small to finite density, and the virial radius corresponds to a cross-over from monatomic to polyatomic gas. Our results have consequences for the search of a low density, low temperature solid-gas phase transition, consistent with the Lee-Yang theorem for lattice gases and with the continuum Widom-Rowlinson mode.

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